A car dealer who sells only late-model luxury cars recently hired a new salesman and believes that this salesman is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesman's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?
Business · High School · Mon Jan 18 2021
Answered on
The appropriate test statistic to determine if the new salesman's average markup is significantly lower than the long-run average markup can be calculated using the formula for a one-sample z-test:
Z = X − μ / σ/n
Where:
X is the sample mean ($5,000)
μ is the population mean (long-run average markup, $5,600)
σ is the population standard deviation ($800)
n is the sample size (16)
Let's compute the test statistic:
Z = 5000 - 5600 / 800/16
Z = -600/ 800/4
Z = -600 / 200
Z = -3
Therefore, the value of the appropriate test statistic for the car dealer to test his claim is
Z= −3.